Pith Number

pith:VRGVL6UF

pith:2026:VRGVL6UFXOBLYGUK5EEZFAOWOS

not attested not anchored not stored refs pending

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs

Philip Hierhager

arxiv:2606.05973 v1 · 2026-06-04 · math-ph · math.DS · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VRGVL6UFXOBLYGUK5EEZFAOWOS}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-06-05T01:15:29.134686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac4d55fa85bb82bc1a8ae9099281d6749500fed269175656bdcf04c5d3c3ac73

Aliases

arxiv: 2606.05973 · arxiv_version: 2606.05973v1 · doi: 10.48550/arxiv.2606.05973 · pith_short_12: VRGVL6UFXOBL · pith_short_16: VRGVL6UFXOBLYGUK · pith_short_8: VRGVL6UF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VRGVL6UFXOBLYGUK5EEZFAOWOS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ac4d55fa85bb82bc1a8ae9099281d6749500fed269175656bdcf04c5d3c3ac73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77388475c1bfe6948fdaf5f2f764e2032c9c5e52d05cad008c50deb8854417cd",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-04T10:15:51Z",
    "title_canon_sha256": "2747e357b0b3daaf4035725cd595b31d1042476d71f19859b2666c5c91086002"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05973",
    "kind": "arxiv",
    "version": 1
  }
}